The edge of a cube is increasing at a rate of 7 cm/s. The rate of change of area of the cube when edge of the cube is 3 cm is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $252\, cm^2/s$
Let the edge of the cube be $x$ cm.
Surface area of cube: $A = 6x^2$
Given: $\frac{dx}{dt} = 7 \, \text{cm/s}$
Differentiate w.r.t. time $t$:
$\frac{dA}{dt} = 12x \frac{dx}{dt}$
Substitute $x = 3$ and $\frac{dx}{dt} = 7$:
$\frac{dA}{dt} = 12(3)(7) = 252$
Final Answer:
$\frac{dA}{dt} = 252 \, \text{cm}^2/\text{s}$